Commentary on the Philosophy of Nature, Chapter 13
The Number of the Planets — an Accusation Standing on Its Head
The anecdote is the best known one in the philosophy of nature, and it does not survive scrutiny. Karl Popper put it this way: Hegel had “deduced, from the philosophy of nature, that no planet could exist between Mars and Jupiter, and offered this deduction as proof of the excellence of his method. It seems that Hegel never referred to the fact… that this planet [Ceres] had been discovered previously, on the first day of the nineteenth century.”
What was actually known in 1801. Piazzi observed the object on January 1, 1801, and was able to track it across nine degrees — two and a half percent of its orbit. He initially took it for a comet and only in passing considered that it might be the planet predicted by the Titius-Bode series. Whether it was a planet or a comet could not be decided with the data available at the time; spectral analysis did not yet exist. Gauss calculated the orbit over the course of the year and communicated the result by letter; he did not publish it until 1809. Olbers recovered the object on December 7, 1801 — before that, it was not even certain that it still existed. Lalande, too, did not regard Gauss’s calculation as proof, since it was extremely sensitive to the smallest measurement errors.
Hegel’s habilitation thesis appeared in August 1801. At that point there was no discovered planet, only an object of unclear nature that no one had seen since February.
What Hegel actually wrote. The Latin text is unambiguous, and it settles the matter.[1]
First, the objection to the Titius-Bode series: “Quae progressio quum arithmetica sit, et ne numerorum quidem ex se ipsis procreationem i. e. potentias, sequatur, ad philosophiam nullomodo pertinet.” — Since this progression is arithmetic, and does not even follow from the generation of numbers out of themselves, that is, from powers, it belongs in no way whatsoever to philosophy.
He then cites a series from Plato’s Timaeus — 1, 2, 3, 4, 9, 16, 27 — and states explicitly that Timaeus does not even apply it to the planets (“quos Timaeus non ad Planetas quidem refert”), but to the proportion according to which the demiurge formed the universe.
And then comes the sentence on which everything turns: “Quae series si verior naturae ordo sit, quam illa arithmetica progressio, inter quartum et quintum locum magnum esse spatium, neque ibi planetam desiderari apparet.” — If this series were the truer order of nature than that arithmetic progression, then it would appear that between the fourth and fifth places there lies a great gap, and that no planet is to be missed there.
This is a conditional clause. Hegel does not prove that no planet could be there — he says what would follow if one were to prefer the one series to the other. And he sets the two series against each other without deciding in favor of either.
Popper turned this into a proof the text does not make. His objection to the Titius-Bode series is twofold, and both parts are the opposite of what he is accused of.
First, he faults it for lacking empirical grounding — precisely at the point where it claims the most. The series requires a planet between Mars and Jupiter; when Hegel wrote, none had been discovered. So he accuses it of exactly what has been held against him for two hundred years: that it overreaches experience.
Second, he faults it for lacking inner necessity. It is a numerical sequence that happens to fit without being able to give any reason why.
The combination of the two objections is the real point: a series that was only empirically grounded, without conceptual necessity — and that, at the one point where it went beyond experience, contradicted the facts. The series is today regarded as a numerical coincidence without physical content.
And Hegel later addressed this explicitly. In the addition to § 270, he states plainly that the distances cannot be derived from the concept but must be taken from experience. This is precisely what Popper missed — while accusing Hegel of having missed something.
How he incorporates the discovery. The same note reads: “Since there is suddenly a great leap from Mars to Jupiter, one did not have a + 4b until, in more recent times, the four smaller planets were discovered — Vesta, Juno, Ceres, and Pallas — which then fill this gap and form a new group. Here the unity of the planet has splintered into a multitude of asteroids, all of which have roughly the same orbit; at this fifth position, fragmentation, being-outside-one-another, predominates.”
He knows of these celestial bodies, then, incorporates them, and interprets them in such a way that they do not appear as an exception but as a distinct group with a character of its own.
What must still be said, nonetheless. That the numerical series appears at all in a philosophical text is the third kind of error from Chapter 2 — the attempt to anchor in a structure something that does not follow from it. But it is a different error from the one he is charged with, and a smaller one. [KF]
Dissertatio philosophica de orbitis planetarum (1801): GW 5, pp. 250 f. The habilitation thesis appears there in full, together with the twelve theses of the disputation. ↩︎